Question

If the area of an equilateral triangle is 81 73 m^2, find its height.​

Answer 1

Answer:

9√3

Step-by-step explanation:

Let the side length be 'S'. And height of the triangle be 'h'.

In any triangle, area = ½ x base x height.

Moreover, specifically, area of equilateral triangle is √(3)/4 x side².

So, here, √(3)/4 x S² = 81√3 m^2

S = 18 m

Note that in this case, base = a whole side of triangle = 18 m.

Using area = ½ x base x height.

=> 81√3 = ½ x 18 x h

=> 9√3 = h

Height of the triangle is 9√3 m.

Answer 2

Answer:

✪ Given :-

• The area of an equilateral triangle is 81√3 m³ .

✪ To Find :-

• What is the height of an equilateral triangle.

✪ Solution :-

» Let, each side of an equilateral triangle be a cm

» Area of an equilateral triangle = 81√3 cm²

➔ We know that,

✯ The area of an equilateral triangle is $\dfrac{√3}{4}$(side)² ✯

➣ According to the question,

⇒ 81√3 = $\dfrac{√3}{4}$ × a²

⇒ a² = 81 × 4

⇒ a² = 324

⇒ a = $\sqrt{324}$

➠ a = 18 cm

Now, we have to find the value of height,

⇒ $\dfrac{√3}{2}$(side)

By putting the value of we get,

⇒ $\dfrac{√3}{2}$(18)

➥ 9$\sqrt{3}$

$\therefore$ The value of the height of an equilateral triangle is 9$\sqrt{3}$ .

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